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 A note on ternary cyclotomic polynomials Bull. Korean Math. Soc. 2014 Vol. 51, No. 4, 949-955 https://doi.org/10.4134/BKMS.2014.51.4.949Published online July 1, 2014 Bin Zhang Nanjing Normal University Abstract : Let $\Phi_n(x)=\sum_{k=0}^{\phi(n)}a(n,k)x^k$ denote the $n$-th cyclotomic polynomial. In this note, let $p < q < r$ be odd primes, where $q \not\equiv 1\pmod p$ and $r\equiv -2\pmod {pq}$, we construct an explicit $k$ such that $a(pqr,k)=-2$. Keywords : cyclotomic polynomial, coefficients of cyclotomic polynomial, ternary cyclotomic polynomial MSC numbers : 11B83, 11C08, 11N56 Downloads: Full-text PDF